Precedent-Informed Reasoning: Mitigating Overthinking in Large Reasoning Models via Test-Time Precedent Learning

TL;DR

This paper introduces Precedent Informed Reasoning (PIR), a method that leverages past related cases to guide large language models during reasoning, reducing redundant exploration and improving efficiency without sacrificing accuracy.

Contribution

PIR is a novel approach that combines adaptive precedent selection and test-time experience internalization to enhance reasoning efficiency in large language models.

Findings

PIR shortens reasoning traces while maintaining or improving accuracy.

PIR achieves better accuracy-efficiency trade-offs across multiple tasks.

Experiments demonstrate PIR's effectiveness in mathematical reasoning, scientific QA, and code generation.

Abstract

Reasoning in Large Language Models (LLMs) often suffers from inefficient long chain-of-thought traces with redundant self-exploration and validation, which inflate computational costs and even degrade performance. Inspired by human reasoning patterns where people solve new problems by leveraging past related cases to constrain search spaces and reduce trial-and-error, we propose Precedent Informed Reasoning (PIR) transforming LRMs'reasoning paradigm from exhaustive self-exploration to guided learning from precedents. PIR addresses two key challenges: what precedents to adopt and how to utilize them. First, Adaptive Precedent Selection (APS) constructs, for each question and LRM, a compact set of precedents that are both semantically related and informative for the model. It ranks examples by a joint score with semantic similarity and model perplexity, then adapts the amount of precedents to maximize perplexity reduction. Second, Test-time Experience Internalization (TEI) is treated as the test-time learning on precedent-informed instruction, updating lightweight adapters to internalize solution patterns and use them as a prior during subsequent reasoning. Experiments across mathematical reasoning, scientific QA, and code generation demonstrate that PIR consistently shortens reasoning traces while maintaining or improving final accuracy across LLMs, yielding outstanding accuracy-efficiency trade-offs.